How do you know whether to put 'de', 'à' or the infinitive after a verb?

The best way to make sure that you know what prepositions follow verbs is to memorise the most commonly used verbs and their prepositions. Vebrs that are commonly used followed by 'de' are 'essayer de', 'décider de' and 's'arrêter de'.
Some of the most common verbs followed by 'à' are 'commencer à', 'aider à' and 'continuer à'.
Verbs that require no preposition are some of the most common such as 'aimer', 'aller', 'venir' and so on.